Modifications of Newton-Cotes formulas for computation of repeated integrals and derivatives
Czechoslovak Mathematical Journal (2023)
- Volume: 73, Issue: 4, page 1175-1188
- ISSN: 0011-4642
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topTvrdá, Katarína, and Novotný, Peter. "Modifications of Newton-Cotes formulas for computation of repeated integrals and derivatives." Czechoslovak Mathematical Journal 73.4 (2023): 1175-1188. <http://eudml.org/doc/299534>.
@article{Tvrdá2023,
abstract = {Standard algorithms for numerical integration are defined for simple integrals. Formulas for computation of repeated integrals and derivatives for equidistant domain partition based on modified Newton-Cotes formulas are derived. We compare usage of the new formulas with the classical quadrature formulas and discuss possible application of the results to solving higher order differential equations.},
author = {Tvrdá, Katarína, Novotný, Peter},
journal = {Czechoslovak Mathematical Journal},
keywords = {repeated integral; Cauchy formula for repeated integration; quadrature; cubature; numerical differentiation},
language = {eng},
number = {4},
pages = {1175-1188},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Modifications of Newton-Cotes formulas for computation of repeated integrals and derivatives},
url = {http://eudml.org/doc/299534},
volume = {73},
year = {2023},
}
TY - JOUR
AU - Tvrdá, Katarína
AU - Novotný, Peter
TI - Modifications of Newton-Cotes formulas for computation of repeated integrals and derivatives
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 4
SP - 1175
EP - 1188
AB - Standard algorithms for numerical integration are defined for simple integrals. Formulas for computation of repeated integrals and derivatives for equidistant domain partition based on modified Newton-Cotes formulas are derived. We compare usage of the new formulas with the classical quadrature formulas and discuss possible application of the results to solving higher order differential equations.
LA - eng
KW - repeated integral; Cauchy formula for repeated integration; quadrature; cubature; numerical differentiation
UR - http://eudml.org/doc/299534
ER -
References
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